What is the derivative of e^{0.1t-1}(5+t) ?

The derivative of e^{0.1t-1}(5+t) is 0.1e^{0.1t-1}t+1.5e^{0.1t-1}

What is the first derivative of e^{0.1t-1}(5+t) ?

The first derivative of e^{0.1t-1}(5+t) is 0.1e^{0.1t-1}t+1.5e^{0.1t-1}

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derivative of

e^{0.1 t - 1} (5 + t)

0.1 e^{0.1 t - 1} t + 1.5 e^{0.1 t - 1}

Solution steps

\frac{d}{d t} (e^{0.1 t - 1} (5 + t))

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = e^{0.1 t - 1}, g = 5 + t

= \frac{d}{d t} (e^{0.1 t - 1}) (5 + t) + \frac{d}{d t} (5 + t) e^{0.1 t - 1}

\frac{d}{d t} (e^{0.1 t - 1}) = e^{0.1 t - 1} \cdot 0.1

\frac{d}{d t} (5 + t) = 1

= e^{0.1 t - 1} \cdot 0.1 (5 + t) + 1 \cdot e^{0.1 t - 1}

Simplify

e^{0.1 t - 1} \cdot 0.1 (5 + t) + 1 \cdot e^{0.1 t - 1} : 0.1 e^{0.1 t - 1} t + 1.5 e^{0.1 t - 1}

= 0.1 e^{0.1 t - 1} t + 1.5 e^{0.1 t - 1}

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((\frac{n}{sin ( x )}) - 1) l

(5 + 3 cos (x)) (1 - 4 tan (x))

(x - 2) (\frac{1}{x + 2}) (x^{3})

y = (x + x^{2})^{\frac{1}{2}}

What is the derivative of e^{0.1t-1}(5+t) ?
The derivative of e^{0.1t-1}(5+t) is 0.1e^{0.1t-1}t+1.5e^{0.1t-1}
What is the first derivative of e^{0.1t-1}(5+t) ?
The first derivative of e^{0.1t-1}(5+t) is 0.1e^{0.1t-1}t+1.5e^{0.1t-1}